Gibbs free energy, base

Figure 7.13 Classical theory of phase transitions is based on the shape of the Gibbs free energy. The Gibbs free energy associated with the points A, B, C and D in (a) are shown in (b). As the system moves from A to D, the Gibbs free energy changes from a curve with two minima to a curve with one minimum...

Thermodynamic data Data associated with the aspects of a reaction that are based on the thermodynamic laws of energy, such as Gibbs free energy, and the enthalpy (heat) of reaction. 

A catalyst speeds up both the forward and the reverse reactions by the same amount. Therefore, the dynamic equilibrium is unaffected. The thermodynamic justification of this observation is based on the fact that the equilibrium constant depends only on the temperature and the value of AGr°. A standard Gibbs free energy of reaction depends only on the identities of the reactants and products and is independent of the rate of the reaction or the presence of any substances that do not appear in the overall chemical equation for the reaction. 

The calculation is based on the rule of thermodynamics, which states that a system will be in equilibrium when the Gibbs free energy is at a minimum. Cl The objective then is the minimization of the total free energy of the system and the calculation of equilibria at constant temperature and volume or at constant pressure. It is a complicated and lengthy calculation but, fortunately, several computer programs are now available that considerably simplify the task. PI... 

Naslain, R., Thebault, J., Hagenmuller, P., and Bernard, C., The Thermodynamic Approach to Boron CVD Based on the Minimization of the Total Gibbs Free Energy, J. Less Common Metals, 67(1) 85-100 (1979)... 

The application of LCCC to block copolymers is based on the consideration that the Gibbs free energy AGAb of a block copolymer A Bm is the sum of the contributions of block A and block B, AGa and AGb, respectively. 

Brinkley (1947) published the first algorithm to solve numerically for the equilibrium state of a multicomponent system. His method, intended for a desk calculator, was soon applied on digital computers. The method was based on evaluating equations for equilibrium constants, which, of course, are the mathematical expression of the minimum point in Gibbs free energy for a reaction. 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

Typically, solving (5.151) to find fc(oo ) is not the best approach. For example, in combusting systems Srp(0 4)1 < 1 so that convergence to the equilibrium state will be very slow. Thus, equilibrium thermodynamic methods based on Gibbs free-energy minimization are preferable for most applications. 

For nF = 0, we immediately get the relationship between nB and q. We now want to change both uB and nF in a direction that decreases G. More precisely, we will exchange one free for one base variable at a time as long as the Gibbs free energy can be decreased. The last equation can be differentiated as... 

Based on the standard Gibbs free energy of the various oxides, three triple points can be calculated WO2.72. WO2.9, WO2 at about 600°C, W02,9, WO3, WO2 at about 270°C, and WO2, WO2.72, W at 1480°C. Using this data, a phase diagram can be constructed. The stability of the various oxides is shown in Fig. 8.2 with respect to the partial pressures of H2O and H2, and temperature. Because aU of these compositions are equilibrium compositions, any of them can be produced simply by annealing W or WO3 at the given partial pressure ratio and temperature. 

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